The risk is far greater when there's a gun around, especially for children. Also it's a bit disingenuous to compare death figures with self-defense incidents where the outcome may have been simple property theft. Injury would be more appropriate, and even that fails as a comparison.
Nice move the goalposts, that's for children aged 5–14. And since those ages are completely non-standard in the literature, we can be sure the data set was massaged until they could "prove" their point using just that interval.
Texas is the only state in the nation that allows the use of lethal force to protect property, so your other point fails, while, I grant, it's informally allowed to some extent elsewhere.
Pardon my lack of familiarity with "the literature" and its standard age groups. Good of you to immediately dismiss the data as "massaged." I couldn't even view your study.
Don't the ages 5 and 14 strike you as strange? What boundaries do they fall on? Not any standard one I can remember for young children, and 14 is a bit more common, but it's not when you become a teen, or the traditional coming of age which is also generally 13, and more like 16/18/21 in the modern US.
If you've been in the field of science long enough, you learn the smell of bad studies, and this one is patently obvious. But I can look more closely at it if you insist.
As for viewing "my" study, note the "Download Free PDF" button to the upper middle right, all you have to do is supply an email address to do it as a guest. Or ask and I'll put a copy up.
And since your point was couched as a warning to others, another counter is that it's relatively easy to keep your family from joining the bad statistics by gun proofing your kids (which you should do anyway, since you can't control when they might come into contact with one outside your home), and storing your guns responsibly.
The risk is far greater when there's a gun around, especially for children. Also it's a bit disingenuous to compare death figures with self-defense incidents where the outcome may have been simple property theft. Injury would be more appropriate, and even that fails as a comparison.